Question

How do you determine the vertex of this equation f(x)= - 1/2x^2-x+3/2. By completing the square? THanks.

Answer 1

yes. Completing the square will put the equation into vertex form
\[y = m(x-p)^2 + q\]
the vertex will then be (p,q).

Answer 2

How do you complete the squre should of have been the question.

Answer 3

\[ y=-\frac{1}{2}x^2-x + \frac{3}{2}\] becomes
\[-2y=x^2 +2x -3\]
becomes
\[-2y = x^2 +2x +1^2 -1^2 -3\]

\[-2y = \left[x^2 +2x +1^2\right] -1^2 -3\] becomes


\[-2y = \left[(x+1)^2\right] -4\] becomes

\[y = -\frac{1}{2}(x+1)^2 +2\]
p=-1, q=2 vertex =(-1,2)

Answer 4

Thank you very much!